Secret sharing

For cases when the whole secret is known by all participants, see shared secret.

Secret sharing (also called secret splitting) refers to methods for distributing a secret among a group, in such a way that no individual holds any intelligible information about the secret, but when a sufficient number of individuals combine their 'shares', the secret may be reconstructed. Whereas insecure secret sharing allows an attacker to gain more information with each share, secure secret sharing is 'all or nothing' (where 'all' means the necessary number of shares).

In one type of secret sharing scheme there is one dealer and n players. The dealer gives a share of the secret to the players, but only when specific conditions are fulfilled will the players be able to reconstruct the secret from their shares. The dealer accomplishes this by giving each player a share in such a way that any group of t (for threshold) or more players can together reconstruct the secret but no group of fewer than t players can. Such a system is called a (t, n)-threshold scheme (sometimes it is written as an (n, t)-threshold scheme).

Secret sharing was invented independently by Adi Shamir[1] and George Blakley[2] in 1979.

A demonstration of visual cryptography: when two same-sized binary images of apparently random black-and-white pixels are superimposed, the Wikipedia logo appears
  1. ^ Shamir, Adi (1 November 1979). "How to share a secret" (PDF). Communications of the ACM. 22 (11): 612–613. doi:10.1145/359168.359176. S2CID 16321225. Archived (PDF) from the original on 2017-08-10.
  2. ^ Blakley, G.R. (1979). "Safeguarding Cryptographic Keys" (PDF). Managing Requirements Knowledge, International Workshop on (AFIPS). 48: 313–317. doi:10.1109/AFIPS.1979.98. S2CID 38199738. Archived from the original (PDF) on 2018-06-28.